Morita equivalence and duality

TL;DR

This paper proves that compactifications of M(atrix) theory on Morita equivalent noncommutative tori are physically equivalent, extending the duality concept to a broader class of noncommutative geometries.

Contribution

It establishes the physical equivalence of compactifications on Morita equivalent tori, generalizing previous duality conjectures for noncommutative geometries.

Findings

Compactifications on Morita equivalent tori are physically equivalent.

Generalization of non-classical duality for two-dimensional tori.

Supports the broader applicability of noncommutative dualities.

Abstract

It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a generalization of non-classical duality conjectured in [1] for two-dimensional tori.